The arrest occurred in Sag Harbor in the Hamptons, a popular summer destination for celebrities on Long Island.
When officers stopped him, Timberlake’s eyes were “bloodshot and glassy” and a “strong odour of an alcoholic beverage was emanating from his breath”, according to a charging document.
His speech was slowed and he performed poorly on the officers’ sobriety tests, the document said.
He also refused a breathalyser test, it added.
“I had one martini and I followed my friends home,” Timberlake allegedly told the officer who stopped him, according to the BBC’s US partner CBS News.
He was released without bail after being formally charged, and is scheduled to appear virtually in court on 26 July, Suffolk County District Attorney’s Office has said.
Timberlake has previously spoken openly about seeking help for excessive drinking.
On Wednesday, his lawyer Edward Burke Jr told PA Media news agency: “I look forward to vigorously defending Mr Timberlake on these allegations.”
He added: “I will have a lot to say at the appropriate time but am currently awaiting full discovery from the District Attorney’s office.”
Timberlake has been touring the US to promote his sixth album, Everything I Thought It Was, and is due to launch the international leg next month, kicking off with a two-night run in Poland.
His scheduled court date coincides with the start of his world tour at the Tauron Arena in Krakow.
In the state of New York, penalties for charges related to driving while intoxicated include up to a year in jail, a $1,000 (£786) fine and the suspension of a driver’s licence for at least six months.
Timberlake was scheduled to perform two shows in Chicago this weekend, followed by a show in New York’s Madison Square Garden next Tuesday.
A former member of the popular 90s boy band NSYNC, Timberlake is an actor, songwriter and one of the best-selling music artists in the world.
The 10-time Grammy winner is also known for his roles in the films The Social Network and Friends With Benefits.
Timberlake is married to actor Jessica Biel, with whom he shares two children.